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Notice that the high-order 20 bits are all zeros, so this logical address is on page 0, the first page. Suppose instead that the process references memory location 10304. Since the page size is 4096, this reference is to a location on the third page, page 2 (remember that the first page was page 0). The number 10304 in binary is the following: 00000000 00000000 00101000 01000000 The high-order 20 bits now create the binary number 2, so this reference is to page 2. The offset within the page is given by the low-order 12 bits as 2112 (the sum of 2048 and 64 from bits 11 and 6; remember, the first bit is bit 0). Multiplying the page number (2) by the page size (4096) gives 8192, and adding the offset of 2112 gives 10304, the original address. Isn t that clever Now imagine how this works with a page table. The page address becomes an index into the page table. The entry in the page table contains the physical frame number. The system simply substitutes the contents of the page table entry, which is the physical frame number, for the page field of the address, and the result is a complete physical address. Suppose that the frame allocated for page 2 (the third page) of the process is frame 9. The page table entry for page 2 would be the following (remember, there are only 20 bits for the frame address): 00000000 00000000 1001 Now the memory reference to location 10304 will result in the frame address of 9 being substituted for the page address of 2, and the resulting physical address will be this address, which is located in frame 9: 00000000 00000000 10011000 01000000 The physical address is 38976, in the 10th frame (again, the first frame is frame 0). Figure 6-1 shows a representation of the page table for a process. Note that the pages of memory allocated to the process need not be contiguous. The operating system can assign any free frame of memory to a process simply by including the frame in the page table for the process.
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Figure 6-1 Mapping logical address 10304 to physical address 38976 using the page table.
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Virtual Memory using Paging A virtual memory operating system that uses paging will map into the process s page table only those pages of logical memory necessary for the process at a particular time. When a process starts, the OS will map in some number of pages to start. This number of pages is determined by an algorithm that takes into account the number of other processes running, the amount of physical memory in the machine, and other factors. In addition to a frame number, a page table entry also includes several important status bits. In particular, a bit will indicate whether the page mapping is valid. When the OS maps in several frames for a process, the process s code and data are copied into the frames, the frame numbers are written into the several page table entries, and the valid bits for those entries are set to valid. Other entries in the page table, for which no mapping to frames has been made, will have the valid bit set to invalid. As long as the process continues to reference memory that is mapped through the page table, the process continues to execute. However, when the process references a memory location that is not mapped through the page table, the fact that the valid bit for that page is set to invalid will cause the reference to generate a page fault. A page fault causes a trap to the operating system, and the operating system must handle the page fault by: 1 2 3 4 5 6 Locating the required page of code or data from the process image Finding an unused memory frame Copying the required code or data to the frame Adding a mapping of the new frame to the process s page table Setting the valid bit in the new page table entry to valid Restarting the instruction which faulted
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The processing of a page fault can also be more complex, as when all memory is allocated, and some previously allocated page mapping must be replaced. Also, because of the wait for disk I/O in reading the process image into memory, it s likely that another process will be scheduled while the disk I/O completes.
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Virtual Memory Problems and Solutions It s fine that each process has a page table mapping its logical address space to physical memory. However, there are additional problems to solve in real systems, in order to make virtual memory systems work well. First, every reference to memory first requires a reference to the page table, which is also in memory. Right away, even when there is no page fault, using a page table cuts the speed of access to memory by a factor of 2. A solution to this problem is to use an associative memory called a translation lookaside buffer (TLB). An associative memory is a small, expensive, magic piece of hardware that can perform a whole set of comparisons (usually 64 or fewer) at once. As a process is executing, the TLB, which is part of the MMU, maintains the recently accessed page table entries. When the process makes a reference to memory, the MMU submits the page number to the TLB, which immediately returns either the frame for that page, or a TLB miss. If the TLB reports a miss, then the system must read the page table in memory, and replace one of the entries in the TLB with the new page table entry. Virtual memory, and particularly the TLB speedup, works because real programs display the property of locality. That is, for extended portions of a process s execution, the process will access a small subset of its logical address space. Real programs use loops, for example, and arrays and collections, and real programs make reference repeatedly to addresses in the same vicinity. Thus, having immediate access to a relatively small number of pages of the process s total logical address space is sufficient to maintain efficiency of execution. A second problem is that page tables themselves become very bulky in modern systems. Our example, which was realistic, showed 20 bits being used for the page number in a 32-bit address. That means that each process has a logical address space of over one million pages. If a page table entry is 32 bits (typical today), then 4 Mbytes of memory are required for each running process, just for the process s page table! Imagine the problem with the newer 64-bit machines even imagining is difficult! One widely used solution is the multilevel page table, a nested page table. To return to our example, suppose we break the 20-bit page address into two 10-bit fields. Ten bits will represent 1024 entities. The first 10-bit field will be an index into the top-level page table, and the second 10-bit field will be an index into
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